Something is not right.
If you have an 8volt supply, then for the output between 1.25V to 6V, there should always be 1.25V between the adj pin and pin and the output pin.
With 2.67V on the adjust pin, 4.4V out should be impossible.
Any chance of a photo of the test circuit?
Things that could be happening include:
Regulator is oscillating. What sort of capacitor are you using for the 0.1uF and is it mounted right next to the regulator?
Multimeter is not reading low voltages correctly. If you read the voltage of a 1.5V alkaline battery, does it read about 1.5V?
Regulator is still not connected right. When you are working out the pins from the data sheet, do you have the heatsink on the side away from you?
Regulator is damaged. Do you have any spare regulators?
Pot is not connected right. When it is turned down to minimum, does the ADJ pin go down to almost 0V?
Richard.